{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 中心极限定理\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import bernoulli\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (6.0, 6.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "例: 某药厂断言，该厂生产的某药品对医治一种疑难的血液病治愈率为0.8. 医院检验员任取\n",
    "100个服用此药的病人,如果其中多于75个治愈，就接受这一断言，否则就拒绝这一断言.\n",
    "若实际上此药对这种病的治愈是0.8,问接受这一断言的概率是多少？ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 伯努利分布 $E(X) = p, D(X) = pq$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bernoulli: 0.8 0.15999999999999998 -1.5000000000000016 0.250000000000012\n"
     ]
    }
   ],
   "source": [
    "p = 0.8\n",
    "bern_froz = bernoulli(p)\n",
    "mean, var, skewness, kurtosis = bern_froz.stats(moments='mvsk')\n",
    "print(\"bernoulli:\", mean, var, skewness, kurtosis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二项分布$f(x) = \\binom{n}{k}p^k(1-p)^{n-k}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "binom: 80.0 15.999999999999996 -0.15000000000000005 0.0025000000000000027\n"
     ]
    }
   ],
   "source": [
    "# 这里的n不是样本的个数, n重伯努利实验, 而是总体分布的参数\n",
    "n = 100\n",
    "binom_froz = binom(n, p)\n",
    "mean, var, skewness, kurtosis = binom_froz.stats(moments='mvsk')\n",
    "print(\"binom:\", mean, var, skewness, kurtosis)\n",
    "\n",
    "# $\\binom{100}{75}$ print(\"1-cdf(75): \", 1 - binom_froz.cdf(75))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 近似正态分布 $E(X) = np, D(X) = npq$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "norm: 80.0 15.999999999999996 0.0 0.0\n",
      "1-cdf(75):  0.9154342776486644\n"
     ]
    }
   ],
   "source": [
    "# 满足n*p 和 n*(1-p)都大于5, 近似正态分布\n",
    "print(n*p > 5, n*(1-p) > 5)\n",
    "\n",
    "# 正态分布\n",
    "norm_froz = norm(n*p, np.sqrt(n*p*(1-p)))\n",
    "mean, var, skewness, kurtosis = norm_froz.stats(moments='mvsk')\n",
    "print(\"norm:\", mean, var, skewness, kurtosis)\n",
    "\n",
    "print(\"1-cdf(75): \", 1 - norm_froz.cdf(75 - 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SWr38lSQvzg7f/wJ/ZW9K8jdJvp3Jr6sPZXKWzIfnOahr6E1J/maM8e0xxvtWP8n3q0nurarO5xe6Ocnzknwhkx/sV2ax9v/l279vwfb/R5Lsqaq/S/L+TJYpd/T+F/jLVNXNSe5L8oExxlNJzq9eP5vk7iQ75tezaazd/sv+6H9X//uf13ZE19TBJGdXT6dxKMk9Waz9f/n2v2HNn7Xf/2OM74wx7h1j/Eom+/mD2eH735usz/THSf5yjHF+9fr9SR7JZEZzaozx+NxGdm1csv1V9dYkdyUZSY6NMf51noPbZh9P8tqq+lQmPxvvSvJUFmf/P2P7F2n/V9UPZzJLrySfzOSEiWezg/e/N1kBmrJEA9CUwAM0JfAATQk8QFMCD9CUwAM0JfAATQk8QFP/Dxm+Ypci8ed4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 以概率p, 实验size次(重复样本, 样本量), 出现p对应的事件的次数k, n是次数上限, 可以用频率图描述\n",
    "# n次伯努利分布随机变量的和\n",
    "\n",
    "binom_rvs_nd = binom_froz.rvs(size = 10*n)\n",
    "norm_rvs_nd = norm_froz.rvs(size = 10*n)\n",
    "plt.hist(x = binom_rvs_nd, bins=n)\n",
    "plt.hist(x = norm_rvs_nd, bins=n)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 泊松分布 $E(X) = \\lambda, D(X) = \\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "poisson: 10.0 10.0 0.31622776601683794 0.1\n",
      "poisson: 2.0 2.0 0.7071067811865476 0.5\n"
     ]
    }
   ],
   "source": [
    "# 当n趋于无穷大时,即一个时间段分为n个细小的段, 每个细小的段发生某事件(0, 1)\n",
    "# 当lambda(平均发生次数) = np (n很大, p很小时)\n",
    "# 通常当n≧20,p≦0.05时, 二项分布可以使用泊松分布近似\n",
    "# 汽车站台的候客人数\n",
    "n, p = 50, 0.2\n",
    "q = 1-p\n",
    "lam = n*p\n",
    "\n",
    "pois_froz = poisson(lam)\n",
    "mean, var, skewness, kurtosis = pois_froz.stats(moments='mvsk')\n",
    "print(\"poisson:\", mean, var, skewness, kurtosis)\n",
    "\n",
    "pois_xs_nd = np.arange(pois_froz.ppf(0.01), pois_froz.ppf(0.99))\n",
    "pois_ys_nd = pois_froz.pmf(pois_xs_nd)\n",
    "binom_ys_nd = binom.pmf(pois_xs_nd, n, p)\n",
    "norm_ys_nd = norm.pdf(pois_xs_nd, n*p, math.sqrt(n*p*q))\n",
    "\n",
    "\n",
    "n2, p2 = 10, 0.2\n",
    "q2 = 1-p2\n",
    "lam2 = n2*p2\n",
    "\n",
    "pois_froz2 = poisson(lam2)\n",
    "mean, var, skewness, kurtosis = pois_froz2.stats(moments='mvsk')\n",
    "print(\"poisson:\", mean, var, skewness, kurtosis)\n",
    "\n",
    "pois_xs_nd2 = np.arange(pois_froz2.ppf(0.01), pois_froz2.ppf(0.99))\n",
    "pois_ys_nd2 = pois_froz2.pmf(pois_xs_nd2)\n",
    "binom_ys_nd2 = binom.pmf(pois_xs_nd2, n2, p2)\n",
    "norm_ys_nd2 = norm.pdf(pois_xs_nd2, n2*p2, math.sqrt(n2*p2*q2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二项分布, 泊松分布, 正态分布的近似"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'n = 10(<=20)')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "fig.set_figwidth(10)\n",
    "ax1.plot(pois_xs_nd, pois_ys_nd,\n",
    "         color='r', lw=2, label='poisson($\\lambda=%d)$' % lam)\n",
    "ax1.plot(pois_xs_nd, binom_ys_nd,\n",
    "         color='g', lw=2, label='binom($n=%d, p=%.1f$)' % (n, p))\n",
    "ax1.plot(pois_xs_nd, norm_ys_nd,\n",
    "         color='b', lw=2, label='norm($\\mu=%d*%.1f, \\sigma=\\sqrt{%d*%.1f*%.1f}$)' % (n, p, n, p, q))\n",
    "ax1.legend()\n",
    "ax1.set_title('n = 50(>=20)')\n",
    "\n",
    "ax2.plot(pois_xs_nd2, pois_ys_nd2,\n",
    "         color='r', lw=2,\n",
    "         label='poisson($\\lambda=%d)$' % lam2)\n",
    "ax2.plot(pois_xs_nd2, binom_ys_nd2,\n",
    "         color='g', lw=2,\n",
    "         label='binom($n=%d, p=%.1f$)' % (n2, p2))\n",
    "ax2.plot(pois_xs_nd2, norm_ys_nd2,\n",
    "         color='b', lw=2,\n",
    "         label='norm($\\mu=%d*%.1f, \\sigma=\\sqrt{%d*%.1f*%.1f}$)' % (n2, p2, n2, p2, q2))\n",
    "ax2.legend()\n",
    "ax2.set_title('n = 10(<=20)')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
